3. (20 points) The following network shows PERT time estimates (optimal, most likely, pessimistic) in weeks. (5,7,9) E (2,4,11), C (1,3,6) G O3.67 D (3,7,12) B (1,7,9) H F (5,8,13) 4 6 (8,8,8) (a) (12 points) Determine a critical path based on most likely times. What is the mean and standard deviation of the length of the critical path? (b) (4 points) Assuming that the critical path is the one identified in a, find the probability that the project will be completed within 33 days. (c) (4 points) Assuming that the critical path is the one identified in a, how many weeks are required to complete the project with probability 0.96? P